A new formal solution of the radiative transfer in arbitrary velocity fields

TL;DR

This paper introduces a novel formal solution to the radiative transfer equation that effectively handles arbitrary velocity fields, ensuring positive generalized opacity and enabling accurate modeling of complex astrophysical phenomena.

Contribution

The authors develop a new formal solution for radiative transfer that maintains positive opacity in non-monotonic velocity fields, improving modeling accuracy in astrophysical applications.

Findings

Relative deviations from established solutions are below 1%.

The new method effectively prevents negative opacities in complex velocity fields.

Applicable to multidimensional radiative transfer in astrophysics.

Abstract

We present a new formal solution of the Lagrangian equation of radiative transfer that is useful in solving the equation of radiative transfer in the presence of arbitrary velocity fields. Normally a term due to the inclusion of the wavelength derivative in the Lagrangian equation of radiative transfer is associated with a generalised opacity. In non-monotonic velocity fields, this generalised opacity may become negative. To ensure that the opacity remains positive, this term of the derivative is included in the formal solution of the radiative transfer problem. The new definition of the generalised opacity allows for a new solution of the equation of radiative transfer in the presence of velocity fields. It is especially useful for arbitrary velocity fields, where it effectively prevents the occurrences of negative generalised opacities and still allows the explicit construction of the Lambda-operator of the system needed for an accelerated Lambda-iteration. We performed test calculations, where the results of old, established solutions were compared with the new solution. The relative deviations never exceeded 1% and so the new solution is indeed suitable for use in radiative-transfer modelling. Non-monotonic velocity fields along photon paths frequently occur in three-dimensional hydrodynamical models of astrophysical atmospheres. Therefore, the formal solution will be of use for multidimensional radiative transfer and has immediate applications in the modelling of pulsating stars and astrophysical shock fronts.